The cost price of 20 articles equal the selling price of x articles, if the transaction result to a 25% profit margin, calculate the value of x?

a. 18

b. 25

c. 30

d. None of the above

What's the correct answer?

To solve this problem, let's start by defining the variables:

- Let the cost price of one article be \( C \).
- Therefore, the cost price of 20 articles is \( 20C \).
- Let the selling price of one article be \( S \).
- Since the cost price of 20 articles equals the selling price of \( x \) articles, we can write the equation as:
  \[
  20C = xS
  \]

Given that the transaction results in a 25% profit margin, the selling price \( S \) is related to the cost price \( C \) by:
\[
S = C + 0.25C = 1.25C
\]

Substitute \( S = 1.25C \) into the equation \( 20C = xS \):
\[
20C = x \times 1.25C
\]

We can simplify this by dividing both sides by \( C \) (assuming \( C \) is not zero):
\[
20 = x \times 1.25
\]

Now, solve for \( x \) by dividing both sides by 1.25:
\[
x = \frac{20}{1.25} = 16
\]

Therefore, the value of \( x \) is 16.

Since 16 is not one of the options provided, the correct answer is:
- **d. None of the above**

Would you like further details or have any other questions?

Here are five questions to expand on this topic:
1. What is the formula for calculating profit margin?
2. How would the value of \( x \) change if the profit margin were 50% instead of 25%?
3. Can you explain the relationship between cost price, selling price, and profit margin?
4. What if the cost price of 30 articles equals the selling price of \( y \) articles with a 25% profit margin—what is \( y \)?
5. How does profit margin impact the selling price in a real-world scenario?

**Tip:** Always check if the answer options provided match the calculated result, especially in multiple-choice questions!

Learn how to calculate the selling price from the cost price and profit margin in this math problem. Understand the relationship between cost price, selling price, and profit margin with a step-by-step solution. Suitable for high school students.

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